Recent content by John3509

  1. J

    B Horner's method confusion

    But that's just the polynomial remainder theorem , which involves polynomial division, horners method just reformats a polynomial into a nest of linear terms. In that section it says "Using Horner's method, divide out ( x − z...
  2. J

    B Horner's method confusion

    I know what synthetic division is and what its point is, its an algorithm that allows you to do polynomial division in a more compact way, by not having to write the variable and its powers. Its how it relates to Horner's method, the reformatting a polynomial into a recursive nest of linier...
  3. J

    B Horner's method confusion

    So I was trying to understand Horner's method. I understand that you can take a polynomial and factor out the x's and re write it as multiple linear functions recursively plugged into each other and that this makes evaluating a polynomial easier because you just evaluate a linear function...
  4. J

    B Help understanding continuing fractions

    I think I get it, although the Newton Raphson method may not be able to be written as a continued fraction what Im thinking of nesting in general, since in the place of x_0 you can plug in the formula with x0-1 and repeat. You cant solve (x^2)-5=0 as a continued fraction tho, i tried (x*x)=5 ...
  5. J

    B Help understanding continuing fractions

    I overlooked your original post because my knowledge of sequences and series is poor. Am I going to have to put my investigation of continued fractions on hold till I learn that? But from the looks of it, it can be done. I stopped the fraction at 5 iterations and computed it and got a very...
  6. J

    B Help understanding continuing fractions

    I know how to turn the mixed number into the continued fraction. I am talking about going the other way. This is the only way I can see a continued fraction be useful for computing something. Lets say you don't know the value is ##\frac{157}{68}## and that is what you are trying to find. Some...
  7. J

    B Help understanding continuing fractions

    It makes a bit more sense to me now as just a weird way of representing a mixed number, I can imagine it being useful in calculating numbers if you can get the whole numbers in the denominator nest you can write out the repeated fraction and simplify it to get the number. But, how then do you...
  8. J

    B Help understanding continuing fractions

    That sounds vaguely similar to a certain method for computing logs, https://www.quora.com/How-can-we-calculate-the-logarithms-by-hand-without-using-any-calculator The first reply. But I do not understand your response. What context would you compute that certain number? Trying to find a...
  9. J

    B Help understanding continuing fractions

    They are mysterious to me, they do not make any intuitive sense. What is the context for them? I found this website. http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/cfINTRO.html It tries to show the history of how they were discovered geometrically. So you start off with a...
  10. J

    B I do not understand Log tables

    Thank you for the answers.
  11. J

    B I do not understand Log tables

    Like here ? http://osf1.gmu.edu/~jschreif/math/math.htm But that is not very accurate beyond the first 2 decimals.
  12. J

    B I do not understand Log tables

    Regarding the scaling, shouldn't it be log[(100010000)(.00000001)]+log[(100020001)(.00000000)] ? How does he scale down? I expected that the values would decrease every step on the table, instead they decreased about every other step, the differenced between the first 2 values was .0043, the...
  13. J

    B I do not understand Log tables

    I suspected it might have something to do with precision since the over all trend was still decreasing, just not how I expect it, I just couldn't figure out how to get so many significant figures? Did you search for some high precision calculator online? What about without calculators, if you...
  14. J

    B I do not understand Log tables

    I was watching this video about how they invented log tables and some things I do not understand. At 5:12 he changes the scaling from 1's to 10's I don't understand how this is allowed. The number represents the number of times the base was multiplied by itself. In the seconds before this...
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